This is a slab of thickness k from Z^3.Īt time 0 each vertex is assigned value 1 or -1 with equal probability We consider zero temperature Glauber dynamics on the vertices of the the When β = 2, this dynamics coincides with that given by the space-time correlation functions constructed by Spohn, Johansson, and others. In particular, we detect the infinite-dimensional stochastic differential equations describing the stochastic dynamics related to Airy random point fields with β = 1,2,4. All canonical Gibbs measures with Ruelle's class interaction potentials (satisfying suitable marginal assumptions) are covered by our theorems. Typical examples are Dyson, Airy, and Bessel random point fields, and the Ginibre random point field. In fact, the associated unlabeled dynamics are reversible with respect to random point fields related to random matrices. We give general theorems to construct unique, strong solutions of infinite-dimensional stochastic differential equations describing IBMs in infinite-dimensions.Īs applications, we construct infinite-dimensional labeled dynamics arising from random matrices. Moving in R d with interaction potentials. Interacting Brownian motions (IBMs) in infinite-dimensions are infinitely many Brownian particles
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Generalized target and generalized misanthrope models.įinally I will explain how to deal with attractivenessįor exclusion processes with speed change, and for I will present examples of generalized zero-range, To determine the extremal invariant and translation invariant Increasing coupling we have constructed, and how it permits Under attractiveness conditions, I will explain the With k ≥ 1, and the jump rate depends on the number K particles may jump from a site x to another site y, Under necessary and sufficient conditions forĪttractiveness. They are conservative particle systems on Z d for which the “basic coupling” construction is not possible
I will mainly focus on generalized misanthrope models. Infinitesimal generator, that stay ordered as soon as I will speak of joint works with Thierry Gobron (CNRS,Ĭergy-Pontoise) and Lucie Fajfrova (UTIA, Prague).Īttractiveness for particle systems corresponds to theĮxistence of a coupling of two processes with the same
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